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mathematics
precalculus

Precalculus 9th edition Michael Sullivan - Solutions

If an object weighs m pounds at sea level, then its weight W (in pounds) at a height of h miles above sea level is given approximately by(a) If Amy weighs 120 pounds at sea level, how much will she weigh on Pike€™s Peak, which is 14,110 feet above sea level?(b) Use a graphing utility to graph
In problem:(a) Find the domain of each function.(b) Locate any intercepts.(c) Graph each function.(d) Based on the graph, find the range.(e) Is f continuous on its domain? f(x) = 1 + x 2 t if x < 0 if x 0
In problem, determine algebraically whether each function is even, odd, or neither.g(x) = -3x3 - 5
In problem, determine (algebraically) whether the given function is even, odd, or neither.f(x) = x/1 + x2
Suppose that the x-intercepts of the graph of y = f(x) are -5 and 3.(a) What are the x-intercepts of the graph of y = f(x + 2)?(b) What are the x-intercepts of the graph of y = f(x - 2)?(c) What are the x-intercepts of the graph of y = 4f (x)?(d) What are the x-intercepts of the graph of y = f(-x)?
In problem, determine whether the equation defines y as a function of x.y = 2x2 - 3x + 4
The graph of two functions, f and g, is illustrated. Use the graph to answer parts (a)€“(f).(a) (f + g)(2)(b) (f + g)(4)(c) (f - g)(6)(d) (g - f)(6)(e) (f - g)(2)(f) (f/g) (4) Уд fy=g(x) (2, 2) (4, 1) (6, 1) 2 2, 1) ( (6, 0) 2 4 Гу-fx) (5, -2) (4, –3) -2 (3, –2. -4-
In problem:(a) Find the domain of each function.(b) Locate any intercepts.(c) Graph each function.(d) Based on the graph, find the range.(e) Is f continuous on its domain? f(x) = Vx if x < 0 if x 0
In problem, determine algebraically whether each function is even, odd, or neither.h(x) = 3x3 + 5
In problem, determine (algebraically) whether the given function is even, odd, or neither.g(x) = 1 + x2/x3
In problem, determine whether the equation defines y as a function of x.y = 3x – 1/x + 2
Suppose that the x-intercepts of the graph of y = f(x) are -8 and 1.(a) What are the x-intercepts of the graph of y = f(x + 4)?(b) What are the x-intercepts of the graph of y = f(x - 3)?(c) What are the x-intercepts of the graph of y = 2f(x)?(d) What are the x-intercepts of the graph of y = f(-x)?
Describe how you would proceed to find the domain and range of a function if you were given its graph. How would your strategy change if you were given the equation defining the function instead of its graph?
In problem:(a) Find the domain of each function.(b) Locate any intercepts.(c) Graph each function.(d) Based on the graph, find the range.(e) Is f continuous on its domain? f(x) = xl if 2 = x < 0 if x > 0
In problem, determine algebraically whether each function is even, odd, or neither.F(x) = 3√x
In problem, use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing.f(x)= 2x3 - 5x + 1 (-3, 3)
In problem, determine whether the equation defines y as a function of x.2x2 + 3y2 = 1
Suppose that the function y = f(x) is increasing on the interval ( -1, 5).(a) Over what interval is the graph of y = f(x + 2) increasing?(b) Over what interval is the graph of y = f(x - 5) increasing?(c) What can be said about the graph of y = - f(x)(d) What can be said about the graph of y = f(-x)?
How many x-intercepts can the graph of a function have? How many y-intercepts can the graph of a function have?
In problem:(a) Find the domain of each function.(b) Locate any intercepts.(c) Graph each function.(d) Based on the graph, find the range.(e) Is f continuous on its domain? f(x) (2 - x lVx if -3 x < 1 if x > 1
In problem, determine algebraically whether each function is even, odd, or neither.G(x) = √x
In problem, use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing.f(x) = -x3 + 3x - 5 (-3, 3)
In problem, determine whether the equation defines y as a function of x.x2 - 4y2 = 1
Suppose that the function y = f(x) is decreasing on the interval (-2, 7).(a) Over what interval is the graph of y = f(x + 2) decreasing?(b) Over what interval is the graph of y = f(x - 5) decreasing?(c) What can be said about the graph of y = -f(x)(d) What can be said about the graph of y = f(-x)?
Is a graph that consists of a single point the graph of a function? Can you write the equation of such a function?
In problem:(a) Find the domain of each function.(b) Locate any intercepts.(c) Graph each function.(d) Based on the graph, find the range.(e) Is f continuous on its domain?f(x) = 2 int(x)
In problem, determine algebraically whether each function is even, odd, or neither.f(x) = x + |x|
In problem, use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing.f(x) = 2x4 - 5x3 + 2x + 1 (-2, 3)
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = 3x2 + 2x - 4
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.f(x) = x2 - 1
Match each of the following functions with the graph that best describes the situation.(a) The cost of building a house as a function of its square footage(b) The height of an egg dropped from a 300-foot building as a function of time(c) The height of a human as a function of time(d) The demand for
In problem:(a) Find the domain of each function.(b) Locate any intercepts.(c) Graph each function.(d) Based on the graph, find the range.(e) Is f continuous on its domain?f(x) = 2 int(2x)
In problem, determine algebraically whether each function is even, odd, or neither.f(x) = 3√2x2 + 1
In problem, use a graphing utility to graph each function over the indicated interval. Approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing.f(x)= -x4 + 3x3 - 4x + 3 (-2, 3)
In problem, find the domain of each function.q(x) = √-x - 2
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.g(x) = 1/2
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.f(x) = x2 +4
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = -2x2 + x - 1
Match each of the following functions with the graph that best describes the situation.(a) The temperature of a bowl of soup as a function of time(b) The number of hours of daylight per day over a 2-year period(c) The population of Florida as a function of time(d) The distance traveled by a car
In problem, the graph of a piecewise-defined function is given. Write a definition for each function. y (2, 1) (-1, 1) . (0, 0) -2
In problem, determine algebraically whether each function is even, odd, or neither.g(x) = 1/x2
In problem, find the average rate of change of f:(a) From 1 to 2(b) From 0 to 1(c) From 2 to 4f(x) = 8x2 – x
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = x/x2 + 1
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.g(x) = x3 + 1
Consider the following scenario: Barbara decides to take a walk. She leaves home, walks 2 blocks in 5 minutes at a constant speed, and realizes that she forgot to lock the door. So Barbara runs home in 1 minute.While at her doorstep, it takes her 1 minute to find her keys and lock the door.Barbara
In problem, the graph of a piecewise-defined function is given. Write a definition for each function. y 2 (2, 1) |(0, 0) -2 (-1, –1) |
In problem, find the average rate of change of f:(a) From 1 to 2(b) From 0 to 1(c) From 2 to 4f(x) = 2x3 + x
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = x2 – 1/x + 4
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.g(x) = x3 - 1
Consider the following scenario: Jayne enjoys riding her bicycle through the woods. At the forest preserve, she gets on her bicycle and rides up a 2000-foot incline in 10 minutes. She then travels down the incline in 3 minutes. The next 5000 feet is level terrain and she covers the distance in 20
In problem, the graph of a piecewise-defined function is given. Write a definition for each function. У 2 (1, 1) (-1, 1) (0, 0) (2, 0) х -2
In problem, determine algebraically whether each function is even, odd, or neither.h(x) = -x3/3x2 - 9
In problem, find the average rate of change from 2 to 3 for each function f. Be sure to simplify.f(x) = 2 - 5x
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = |x| + 4
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.h(x) = √x -
In problem, the graph of a piecewise-defined function is given. Write a definition for each function. y (0, 2), (2, 2) (1, 1) (-1, 0) -2 2 X
In problem, determine algebraically whether each function is even, odd, or neither.F(x) = 2x/|x|
In problem, find the average rate of change from 2 to 3 for each function f. Be sure to simplify.f(x) = 2x2 + 7
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = √2x2 + x
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.h(x) = √x +
The following sketch represents the speed Ï… (in miles per hour) of Michael€™s car as a function of time t (in minutes).(a) Over what interval of time was Michael traveling fastest?(b) Over what interval(s) of time was Michael€™s speed zero?(c) What was
If f(x) = int(2x), find(a) f(1.2)(b) f(1.6)(c) f(-1.8)
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. УА (1, 4) (3, 3) (2, 2) (5, 1) X. 2.
In problem, find the average rate of change from 2 to 3 for each function f. Be sure to simplify.f(x) = 3x - 4x2
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = 2x + 1/3x - 5
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.f(x) = (x –
If f (x) = int(x/2), find(a) f(1.2)(b) f(1.6)(c) f (-1.8)
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. УА (4, 4) |(0, 2) (1, 1) (5, 0) 5 2.
In problem, find the average rate of change from 2 to 3 for each function f. Be sure to simplify.f(x) = x2 - 3x + 2
In problem, find the following for each function:(a) f(0)(b) f(1)(c) f(-1)(d) f(-x)(e) -f(x)(f) f(x + 1)(g) f(2x)(h) f(x + h)f(x) = 1 – 1/(x + 2)2
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.f(x) = (x +
Is there a function whose graph is symmetric with respect to the x-axis? Explain.
Sprint PCS offers a monthly cellular phone plan for $39.99. It includes 450 anytime minutes and charges $0.45 per minute for additional minutes.The following function is used to compute the monthly cost for a subscriber:where x is the number of anytime minutes used. Compute the monthly cost of the
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. Уд (3, 4) 4 |(0, 3) (4, 3) (1, 1) 3
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.g(x) = 4√x
In problem, find the domain of each function.f(x) = -5x + 4
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. УА (2, 4) (1, 3) (0, 1) 3
In problem, find the domain of each function.f(x) = x2 + 2
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. У, 4 (2, 3) (-1,1) (0, 0) (3, 2) 1 3 -1
In problem, is the graph shown the graph of a function? Уд
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.f(x) = -3√x
In problem, find the domain of each function.f(x) = x/x2 + 1
In problem, is the graph shown the graph of a function? Уд
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.f(x) = -√x
In problem, find the domain of each function.f(x) = x2/x2 + 1
Two 2009 Tax Rate Schedules are given in the accompanying table. If x equals taxable income and y equals the tax due, construct a function y = f(x) for Schedule X. REVISED 2009 TAX RATE SCHEDULES Schedule Y-1-Married Filing jointly or qualifying Widow(er) Schedule X-Single Of the Excess Over If
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. Уд (3, 2) 2 - (2, 0) (4, 1) т х -1 1 3 (-2, –2) -2 (-1, -3)
In problem, sketch the graph of each function. Be sure to label at least three points.f(x) = |x|
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.f(x) = 2(x +
In problem, find the domain of each function.g(x) = x/x2 - 16
In problem, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. У (1, 3) 2 (-1, 1) (0, 2) (3, 1) | (2, 0) 3 -1 -2
In problem, sketch the graph of each function. Be sure to label at least three points.f(x) = 3√x
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.f(x) = 3(x -
In problem, find the domain of each function.h(x) = 2x/x2 - 4
A trucking company transports goods between Chicago and New York, a distance of 960 miles. The company’s policy is to charge, for each pound, $0.50 per mile for the first 100 miles, $0.40 per mile for the next 300 miles, $0.25 per mile for the next 400 miles, and no charge for the remaining 160
In problem, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places.f(x) = x3 - 3x + 2 (-2, 2)
In problem, sketch the graph of each function. Be sure to label at least three points.f(x) = √x
In problem, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function.g(x) = 2√x
In problem, find the domain of each function.F(x) = x – 2/x3 + x
An economy car rented in Florida from National Car Rental® on a weekly basis costs $95 per week. Extra days cost $24 per day until the day rate exceeds the weekly rate, in which case the weekly rate applies. Also, any part of a day used counts as a full day. Find the cost C of renting an economy

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